Nonsingular Gradient Solutions in Crack Mechanics and the Concept of Stress Concentration

Abstract

We consider the fracture mechanics problem for the finite and semi-infinite cracks in the gradient elasticity. Local stress fields that define the fracture the strength of materials are found as solutions of the inhomogeneous Helmholtz equations in which the inhomogeneity is determined by classical stresses. To construct solutions, the radial factors method and the Papkovich-Neuber representation are used. It is shown that, in problems of crack mechanics. We show that the local stresses in the vicinity of crack tips are non-singular, have the form characteristic of stress concentration, and depend only on the level of acting stresses and the scale parameter, which is found as a result of mechanical testing of material samples.